Find two numbers whose sum is 27 and product is 182.

Let the first number = x
Therefore, the second number = 27 – x
According to the question,
Product, = x(27 – x) = 182
⇒ 27x – x² = 182
⇒ x² – 27x + 182 = 0
⇒ x² – 13x – 14x + 182 = 0
⇒ x(x -13) – 14 (x -13) = 0
⇒ (x – 13) (x – 14) = 0
⇒ (x – 13) = 0 or (x – 14) = 0
Either x = 13 or x = 14
Hence, the two required numbers are 13 and 14